{"paper":{"title":"Critical density of activated random walks on transitive graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alexandre Stauffer, Lorenzo Taggi","submitted_at":"2015-12-08T10:49:24Z","abstract_excerpt":"We consider the activated random walk model on general vertex-transitive graphs. A central question in this model is whether the critical density $\\mu_c$ for sustained activity is strictly between 0 and 1. It was known that $\\mu_c>0$ on $\\mathbb{Z}^d$, $d\\geq 1$, and that $\\mu_c<1$ on $\\mathbb{Z}$ for small enough sleeping rate. We show that $\\mu_c\\to 0$ as $\\lambda\\to 0$ in all vertex-transitive transient graphs, implying that $\\mu_c<1$ for small enough sleeping rate. We also show that $\\mu_c<1$ for any sleeping rate in any vertex-transitive graph in which simple random walk has positive spee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02397","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}